Re: The set of necessary FISONs (axiomless natural deduction)

On 2/4/2025 4:59 AM, Ross Finlayson wrote:

On 02/04/2025 01:44 AM, Ross Finlayson wrote:

On 02/03/2025 06:15 PM, Jim Burns wrote:

If there is a mere contingent contrivance which
describes what I'd like described,
I will use it and be grateful for it.

The, "fundamental question of metaphysics",
or, "why is there something rather than nothing",
has [...]
that _strong mathematical platonism_ makes for
that it's possible to arrive at
an axiomless geometry [...]

Mathematics is poorly.suited to addressing
why there is something.
Mathematics addresses all descriptions (roots),
what is, what might be, and what cannot be,
and the consequences growing from descriptions (vines).
Its techniques show us that, from some roots,
vines grow which have bad fruit (contradictions),
We prune vines and roots with bad fruit.
We look for descriptions of what (really) exists
among the unpruned vines.
Being fruit of an unpruned vine is not the same
as describing what exists, although,
it is closer (in some cosmic sense) to existing than
being fruit of a pruned vine.
Mathematics can't tell us what is,
although it can tell us what isn't.
----
In some circumstances,
the vines have been pruned so severely that
very little is left to choose from.
I suppose someone might argue that there, at least,
mathematics tells us what IS, not only what ISN'T.
⎛ I'm thinking of string theory,
⎜ the attempted unification of physical forces.
⎜ If I understand correctly,
⎜ in order for string theory to be consistent,
⎜ there must be eleven dimensions.
⎜ Which appears to be wildly wrong.
⎜ However,
⎜ one proposal is that the extra dimensions are
⎜ curled up tighter than our instruments can detect.
⎜ How would we know they're undetectably existing?
⎜ In this not.yet.realized scenario,
⎜ all the vines without eleven dimensions get pruned,
⎝ mathematically or experimentally.